Models and Algorithms for Addressing Travel Time Variability: Applications from Optimal Path Finding and Traffic Equilibrium Problems

Abstract

An optimal path finding problem and a traffic equilibrium problem are two important, fundamental, and interrelated topics in the transportation research field. Under travel time variability, the road networks are considered as stochastic, where the link travel times are treated as random variables with known probability density functions. By considering the effect of travel time variability and corresponding risk-taking behavior of the travelers, this dissertation proposes models and algorithms for addressing travel time variability with applications from optimal path finding and traffic equilibrium problems. Specifically, two new optimal path finding models and two novel traffic equilibrium models are proposed in stochastic networks. To adaptively determine a reliable path with the minimum travel time budget required to meet the user-specified reliability threshold α, an adaptive α-reliable path finding model is proposed. It is formulated as a chance constrained model under a dynamic programming framework. Then, a discrete-time algorithm is developed based on the properties of the proposed model. In addition to accounting for the reliability aspect of travel time variability, the α-reliable mean-excess path finding model further concerns the unreliability aspect of the late trips beyond the travel time budget. It is formulated as a stochastic mixed-integer nonlinear program. To solve this difficult problem, a practical double relaxation procedure is developed. By recognizing travelers are not only interested in saving their travel time but also in reducing their risk of being late, a α-reliable mean-excess traffic equilibrium (METE) model is proposed. Furthermore, a stochastic α-reliable mean-excess traffic equilibrium (SMETE) model is developed by incorporating the travelers’ perception error, where the travelers’ route choice decisions are determined by the perceived distribution of the stochastic travel time. Both models explicitly examine the effects of both reliability and unreliability aspects of travel time variability in a network equilibrium framework. They are both formulated as a variational inequality (VI) problem and solved by a route-based algorithm based on the modified alternating direction method. In conclusion, this study explores the effects of the various aspects (reliability and unreliability) of travel time variability on travelers’ route choice decision process by considering their risk preferences. The proposed models provide novel views of the optimal path finding problem and the traffic equilibrium problem under an uncertain environment, and the proposed solution algorithms enable potential applicability for solving practical problems.

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